5. A fair six sided die is rolled 10 times. Let X be the number of...
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI
I know Pk~1/k^5/2 just need the work Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
we repeatedly roll a fair 8-sided die six times and suppse X is the number of different values rolled. Find E[x] and E[Y]
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m 7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
6. A fair six sided die is rolled three times. Find the probability that () all three rolls are either 5 or 6 (6) all three rolls are even (c) no rolls are 5 (d) at least one roll is 5 (e) the first roll is 3, the second roll is 5 and the third roll is even
If a die is rolled six times, let X be then number the die obtained on the first roll and Y be the sum of the numbers obtained from all the rolls. Find the expected value and variance of x and y.
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these dice both have the numbers most people would expect on them). Let Z be a random variable that represents the absolute value of their difference. For instance, if a 4 and a 1 are rolled, the corresponding value of Z is 3. (a) What is the pmf of Z? (b) Draw a graph of the cdf of Z
What is the probability that a fair six-sided die rolled five times comes up 6 exactly once?